This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. There have been many single nucleotide polymorphism-based tests suggested for association analysis in a case-control design. The possible evidence for association comprises three types of information: differences between cases and controls in allele frequencies, in parameters for Hardy Weinberg disequilibrium (HWD) and in parameters for linkage disequilibrium (LD). We found the pairwise covariances between statistics that measure these three types of information and show that the statistics are asymptotically trivariate normally distributed. Then we compared their power analytically to determine the most informative statistics according to the disease model. Our results show that differences in parameters for HWD are informative for dominant and recessive disease models, while differences in allele frequencies and in parameters for LD are generally informative except for rare recessive disease models. There is mutual independence of the statistics that detect these three differences under Hardy Weinberg equilibrium at the marker locus and linkage equilibrium between markers in the population. Knowing the pairwise covariances between the statistics makes it possible to define statistics that are mutually independent. This allows us to perform sequential analyses of the same data without the need to adjust significance levels for all the multiple analyses being performed on the same data set. As a result we can have improved flexible strategies to increase the power of genome-wide association studies without requiring the collection of a new, independent sample. In a later study, we have developed a general framework, based on a logistic regression model, that increases power by taking account of all three types of information simultaneously.